Sentence examples for by the identity function from inspiring English sources

In this, the sucessive FFT frames have their amplitudes remapped by the identity function, similiarly expanding or compressing by the dynamic range depending upon the warp specified.

Roughly speaking, to apply this theorem, it is required that the gains composition is continuous, increasing and upper bounded by the identity function.

More specifically, we give operator-theoretic conditions on Mz, where Mz denotes the operator of multiplication by the identity function on D, that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary.

Remark 4.2 If τ ( t ) = q − 1 t, then (4.2) is satisfied by the identity function.

It should be noted that the steady state MSE is high because of the error caused by the fact that the nonlinearities are not approximated (actually they are modeled by the identity function) (Equation (25)).

For each class declaration (mathtt{class },P,Rightarrow overline{alpha },mathtt{where },overline{x}::overline{tau },) a sequence of selection functions is generated, one for each overloaded name in (overline{x}.) The selection function corresponding to (x_i) simply selects the (i -th component of the tuple parameter (..., (x_i -th.) (if (n=1,) selecomponentdofe by the identuplefunction).

We denote by ℓ, the identity function on ([0,1]), namely, (ell (t)=t) ((tin[0,1])); and for (tinOmega), (zetain[a,b]) and (lambdainmathbb{C}), we have mathop{operatorname{ess}sup}_{sin[0,1]} biglvert f" bigl((1-s)zeta+sg(t) 1-s zeta+sgabigrvert =biglVert f" bigl((1-s zeta+sgell g bigr)-lambdabigrVert _{[0,1],infty}.

Therefore, the result follows from Theorem 2.14 immediately by taking f as the identity function.

Therefore, the results follow immediately from Theorem 3.2 by taking f as the identity function.

Therefore, part (i) follows from Theorem 2.21 immediately by taking f as the identity function.

Also, part (ii) follows from Theorem 2.26 immediately by taking f as the identity function.